For a given transistor,if $\alpha = 0.95$,find the common emitter current gain $\beta$.

In an $NPN$ transistor circuit,the collector current is $10 \,mA$. If $90\%$ of the electrons emitted reach the collector,the emitter current $(i_E)$ and base current $(i_B)$ are given by

In the case of constants $\alpha$ and $\beta$ of a transistor:

When a transistor is used as an amplifier in common emitter configuration,which of the following statements are correct?
$(1)$ The base-emitter junction is forward-biased.
$(2)$ The base-emitter junction is reverse-biased.
$(3)$ The input signal is connected in series with the biasing voltage to the base-emitter junction.
$(4)$ The input signal is connected in series with the biasing voltage to the base-collector junction.

From the given transfer characteristic of a transistor in $CE$ configuration,the value of power gain of this configuration is $10^x$,for $R_B = 10\,k\Omega$ and $R_C = 1\,k\Omega$. The value of $x$ is $.....$.

Given below are two statements:
Statement $I :$ $PN$ junction diodes can be used to function as a transistor,simply by connecting two diodes back-to-back,which acts as the base terminal.
Statement $II :$ In the study of transistors,the amplification factor $\beta$ indicates the ratio of the collector current to the base current.
In the light of the above statements,choose the correct answer from the options given below: